CPhill

1.  4 sin^2 x – 1 = 0    add 1 to both sides

4sin^2x  = 1       divide both sides by 4

sin^2 x   = 1/4          take both roots and we have that

sin x = √[1/2 ]  and this happens at  45 degrees and  135 degrees    

And

sin x = - √[1/2]   and this happens at   225 degrees and 315 degrees

See answer here, FA :  https://web2.0calc.com/questions/help-please_29047

[ Age  -  Mean ]

____________   = z score     .....fill in what we know

    Std Dev

[ Age - 35 ]

________     =  -2.1              multiply both sides by  8.2

     8.2

Age  - 35  =  -17.22         add 35 to both sides

Age  =  17.8  years 

[ 105 - 103 ] 

_________      =  z score  ≈  0.74  

    2.7

They are the same thing.....but....since they want two decimal places....try either 0.50  or .50

We're just sticking each number into the function and evaluating, GM....for example

f(3)  =  2(3) - 7  =  6 - 7  =  -1

And

g(3)  = 5^3  =  125

Pretty easy, huh  ????

First one....good job on both parts  !!!!

a.  This looks to be arithmetic.....common difference between terms =2

And the first term = 2

So

a_n  = 2 + 2(n - 1)   which we can simplify as   a_n = 2_n

b. Also arithmetic .....common difference = 2 ....first term = 3

a_n  = 3 + 2(n - 1)     which we can simplify as   a_n  = 2n + 1

c. Arithmetic....common difference = -25  and the first term is 50

a_n  = 50 - 25(n - 1)    =   75 - 25n  

4. Geometric.....common ratio  = 1 / (1/3)  = 3....first term = 1/3

a_n  = (1/3)*3^(n - 1)

That's a nice approach, Melody   !!!

See here, flanspawn  :  https://web2.0calc.com/questions/one-of-my-questions-i-couldnt-get